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FATIGUE CRACK GROWTH IN

IRON SILICON ALLOYS

by

W GEARY

A thesis submitted to the Council for National Academic Awards in partial

fulfilment for the Degree of:

DOCTOR OF PHILOSOPHY IN METALLURGY

Collaborating Establishment:- Sponsoring Establishment:-Sheffield Laboratories Swinden House British Steel Corporation ROTHERHAM

Department of Metallurgy Sheffield City Polytechnic SHEFFIELD

7 9 35 5 9 3-01

It seems to me an art comprising great knowledge, for I know of no art or activity whatever, excluding the sciences and painting, that does not need this as its principal member. Therefore, in my opinion, if it were not for the nobility of the material, I would say that the smith working in iron should justly take precedence over the goldsmith because of the great benefit that he brings.

Vannoccio Biringuccio 1540

CONTENTSPage

INTRODUCTION (ix)1 REVIEW OF LITERATURE 1

1.1 Stress distributions around cracks and 1crack tip plasticity1.1.1 Introduction 11.1.2 Cyclic plastic zone formation 4

1.2 Experimental evidence of plasticity 51.3 Intermediate range fatigue crack growth 7

1.3.1 Models 71.3.2 Mechanisms 101.3.3 Mean stress effects 121.3.3.1 Introduction 12

1.4 Near threshold crack growth models 141.5 Fatigue thresholds 20

1.5.1 Introduction 201.5.2 Mean’stress effects 21

, 1.5.2.1 Introduction 211.5.3 Microstructural factors 241.5.3.1 Material strength 241.5.3.2 Grain size effects and crack 26

tip plasticity1.5.3.2.1 Introduction 261.5.3.2.2 Plasticity effects 291.5.3.3 Effect of grain boundary 31

segregation1.5.3.4 Effect of material purity 321.5.3.5 Microstructure and mechanisms 321.5.3.6 The behaviour of dislocations 361.5.3.6.1 Introduction 361.5.3.7 Crack closure concepts 371.5.4 Environmental aspects of fatigue 39

crack growth'1.5.'4.1 Introduction 391.5.4.2 Influence of microstructure 401.5.4.3 Mechanisms of crack growth in 42

environments

(i)

1.5.4.4 Kinetics of hydrogen effect1.6 Fatigue crack growth of silicon iron

1.6.1 Introduction2 EXPERIMENTAL PROCEDURES

2.1 Materials2.1.1 Chemical composition

, 2.1.2 Mechanical working and heattreatments

2.1.2.1 Aluminium casts2.1.2.2 Upset forging

2.2 Grain size measurements2.3 Tensile properties2.4 Test piece preparation2.5 Crack growth measuring techniques

2.5.1 Introduction2.5.2 Calibration of PD technique2.5.3 Experimental calibration

2.6 : Experimental test equipment andtesting procedure

2.7 Data analysis2.8 Threshold testing2.9 Accuracy of the potential drop

• technique2.10 Residual stress measurements

2.10.1 Introduction2.10.2 Residual stress measurement

technique2.11 Metallography

2.11.1 Optical Microscopy2.11.2 Electron Microscopy

2.12 Texture determinations

Page4546 4650505051

53545456,575858596061

6465 b 6

676767

69696970

(ii)

3 EXPERIMENTAL RESULTS 723.1 Introduction 723.2 Fatigue crack growth rate results 73

3.2.1 Threshold growth results 733.3 Grain size and compositional effects 753.4 Intermediate growth results 763.5 Plastic zone sizes 763.6 Strain hardening exponents 773.7 TEM results 783.8 Fractography 78

3.8.1 Qualitative fractography 783.8.2 Crack branching and secondary 81

cracking3.8.3 Striations 823.8.4 Fatigue fretting 833.8.5 Quantitative metallography 84

3.9 Residual Stress results 843.10 Texture results 85

4 DISCUSSION 864.1 Introduction 864.2 The concept of fatigue threshold 864.3 Fatigue crack growth fractography 87

4.3.1 Model of near threshold growth 884.4 Plasticity and grain size effects on threshold 89

4.4.1 Introduction 894.4.2 Grain size effects 934;4.2.1 Introduction 93

4.5 Crack closure and crack deflection phenomena 944.5.1 Crack closure t 944.5.2 Micromechanisms of crack closure 954.5.3 Oxidation products 954.5.4 Fretting fatigue 96

(111)

Pages4.5.5 Irregular, rough fracture surfaces S7

and facet contact4.5.6 Mode II type opening 984.5.7 Crack deflection effects 101

4.6 Summary 1035 Conclusions 1056 Recommendations for further work 107References 109Case Study 122

147Tables156

Figures

(iv)

Preface

All the work reported in this thesis was carried out during the period for which the candidate was registered for a higher degree.

In accordance with the regulations for PhD in Industrial Metallurgy, a full course in Metallurgical Process and Management was successfully completed. The details of the course are given below

MODULE 1

Process Metallurgy Mechanical Metallurgy iAdvanced Thermodynamics

MODULE 2

AccountancyMicro-economics and Financial Control Computational Methods and Operational Research

MODULE 3

Powder MetallurgyHigh Strength SteelsHeat Treatment and TransformationsAtmospheric Pollution and ControlCorrosion Resistant and High Temperature AlloysAutomatic and Computer Control

(v)

MODULE 4

Industrial Case Studies

One of the case studies, which is related to the current research work, is attached with the thesis, as Appendix 1.

The candidate’s performance during the above mentioned courses was assessed by means of written examinations and continuous assessment of specific assignments.

(vi)

Acknowledgements

The author is heavily indebted to Mr P Leggett, Mr F Walker, and Dr P James for their continuous support, encouragement and advice throughout the duration of the work.

Grateful appreciation is also expressed to the technical staff of the Department of Metallurgy and British Steel Corporation, Swinden Laboratories whose services were invaluable. Special thanks are due to Dr I M Austen and Mr C Lindley.

The author would also like to express his gratitude to Dr A W D Hills, Head of Department of Metallurgy, for provision of facilities for the work. Sincere gratitude is also due to Dr M J May, Research Manager, for provision of facilities at Swinden Laboratories.

(vii)

ABSTRACT

Fatigue Crack Propagation in Iron-Silicon Alloys

byW Geary 1985

A technique for accurately monitoring fatigue crack growth at near threshold growth rates has been established. The characteristics of near threshold fatigue crack growth of a number of iron-silicon alloys has been quantitatively and qualitatively investigated. Relationships have been established relating the stress intensity factor, AK, and the fatigue crack growth rate da/dN. At fatigue crack growth rates approaching threshold the material has shown some microstructural sensitivity and this has been related to the stress intensity factor and the yield stress.A relationship has been shown to exist between the value of the threshold stress intensity^ffnd the inverse root of the grain size, d~ 2 , for each of the alloys investigated. A model for near threshold fatigue crack growth has been proposed and includes the contributions made by grain size and crack tip plasticity.This work has also shown that fatigue crack closure plays an important role in the micromechanisms of fatigue crack growth near the threshold at low R ratio s. A number of mechanisms have been identified: crack closure due tothe presence of oxidation products on fracture surfaces in tests conducted in air,and closure due to the presence of fatigue fretting, facet contact and a contribution of mixed mode opening.

(viii)

INTRODUCTION

Little is currently known about the micromechanisms offatigue crack propagation at near threshold growth rates.It is important from a design point of view that engineeringand metallurgical data of this sort are provided to allowdesign of components and selection of materials, capableof withstanding a large number of cycles at low stress

1 9intensity factor ranges for lifetimes up to 10x* cycles.

Most studies of fatigue crack propagation have confirmedthat the crack growth rate da/dN is a function of the

factoralternating stress intensity^>AK, through the power law expression da/dN = C(AK)n . The expression, however, over estimates the growth rate as AK approaches AK^.

Much work has been done on near threshold fatigue crack growth on a wide variety of materials. However, the majority of data has been obtained on complex alloy systems of direct industrial application. These complex, multiphase, industrial alloys are not ideally suited to the task of determining the basic mechanisms occurring at low fatigue crack growth rates. An iron silicon, single phase, system was considered ideal for the purpose of assessing the effects of variations in grain size on near threshold fatigue crack growth. It was intended during this work to determine the effects of variations in grain size on levelsin terms of the micromechanisms of deformation and fracture occurring at the crack tip.

(ix)

It is known that in pure iron/ homogeneous wavy slip occurs/ s

and that a change to more planar slip is caused by theaddition of silicon to iron. Screw dislocations tend toremain on the (110) planes rather than moving by cross sliponto other planes as in pure iron.

Restricted slip systems are produced in the iron silicon alloys. It was intended during this research to examine the effects of restricted slip systems on near threshold fatigue crack growth rates and the interrelationships between slip behaviour, crack tip plasticity and grain size.

This was to be achieved by the production of a series of iron silicon alloys and the use of thermomechanical treatments to

produce a variable grain size. A number of compact tension fatigue specimens were to be tested in tension - tension fatigue, and monitored by a sensitive technique to produce data relating the effects of grain size and solute concentration to the near threshold fatigue crack growth of these alloys.

(x)

1 REVIEW OF LITERATURE

1.1 STRESS DISTRIBUTION AROUND CRACKS AND CRACK TIP PLASTICITY

1.1.1 INTRODUCTION

The primary variable which dictates whether and at what rate fatigue crack propagation occurs under variable loading conditions is the stress configuration immediately adjacent to the crack tip.

A great deal of work has been concentrated on the solution of elastic and elastic/plastic boundary conditions of statically and cyclically loaded cracks. A comprehensive review of stress and strain distributions around cracks is given in the standard texts1,z .

Using the stress co-ordinate system shown in Figure 1 afterRice3, the elastic stress distribution around a geometricstress concentration under Mode 1 opening is given byFigure 2 (a). Under plane strain conditions where nothrough thickness relaxation can occur, a arises in order* zzto maintain elastic strain continuity. In plane stressthe value of a is zero and the distribution of or is zz xxdiminished as contraction is allowed in the Z direction.The edge of a body, in essentially plane strain, will be in plane stress and the distribution is shown in Figure 2 (b).

The elastic distribution around a crack in Mode 1 opening has been given by Irwin11.

1

Ixz)

0 Generalised plane stress

1

a = v(a + o ) Plane strain z x y

Kj is the stress intensity factor for Mode I type opening and is simply related to the elastic energy release rate. Other equations exist for Modes II and III openings,

and K m .

Once determined, the stress intensity parameter K allows comparison of crack tip elastostatics independent of specimen geometry, crack length or applied stress.

If the ideal case of a crack of length 2a situated in an infinite body subject to a stress aa in Mode I openingis considered then the stress intensity at the crack tipis defined asKj = aa /rfa - 2

In a cracked body of finite dimensions this equation ismodified by a dimensionless geometric parameter, Y, to allow for specific boundary conditions.Kj = Y aa A a - 3

When a body containing a crack is stressed elastically, itis possible to produce high stresses at the crack tip whichmay locally exceed the material's yield stress to producea plastic zone. The occurrence of plasticity under plane

incorporating the respective stress intensity factors

2

strain conditions causes a to rise at a much’ greaterxxrate than would be expected in order to maintain continuity of the elements (Figure 3),

A simple estimation of the size of the plastic zone at the head of the crack under plane strain conditions is given by Irwin4.

The elastic stress distribution shown in Figure 4 (a) is altered by an amount of yielding, Figure 4 (b), which is small compared with the crack length and the dimensions of the body. The plastic zone is considered to extend a small distance ahead of the crack tip. Within this zone the tensile stress o is equal to the yield stress.yy *

An underestimate of the plastic zone size, w, can be obtained by equating o^ with the yield stress (ayS ) ,Figure 4 (c). This is an underestimate as the stress depicted by the shaded area oyy = oyS and

°yy = Ki _ 4/2irr

is available for further yielding.

The magnitude of ry is then given by:-

ry ° fif _ 52"°yS2

The shaded area can be shown to be equal to half the total area under the curve up to r = ry and it has been conventional to equate w to a first approximation as:-

3

W = 2ry = Kj2 6

The plane strain plastic zone is reduced to 1/3 to account for the effects of triaxiality on yielding and therefore the plane strain plastic zone size is given by:-

The elastic stress distribution ahead of a crack can be described by a modified stress intensity factor, K * , where:-

1.1.2 CYCLIC PLASTIC ZONE FORMATION

It is assumed (see Figure 5) that the central region of a thick test piece deforms under plane strain conditions; local yielding occurs around the crack tip; high constraints are set up and a triaxial stress state is developed.

For a given crack opening displacement the plastic zone size in plane stress is much larger than for plane strain because yielding spreads under a shear stress component

which incorporates the full value of the local tensile stress.

The strain gradient in plane strain immediately ahead of the crack is steep and crack extension is easier to achieve.

Figure 6 shows a schematic stress displacement curve for the region immediately ahead of the crack tip during a stress cycle. The specimen is unloaded from the peak of

I \ 2W = 1 Kj \ 2 73lT \ ays y

K* = a /[>(a + ry )] 8

4

the tensile stroke, the local stresses at the crack tip unloaded elastically and then become compressive. Some reverse plastic flow is then obtained when the compressive stresses become equal to the flow stress in compression. The amount of reversed flow at zero overall displacement is given by the amount of flow corresponding to a material with a flow stress 2ayS . Then the reversed plastic zone size can be estimated from:-

W = 1_ 3 tt 2

between plane strain and plane stress, being dependent upon loading and geometrical considerations.

Evidence of the effect of state°fstress on zone shape and magnitude has been provided by several techniques 8> 6.

Weiss and Meyerson 5 using two surface measurement techniques showed that the size and shape of the plastic zone produced by fully reversed bending fatigue is virtually unpredictable but in general they observed zones smaller than theoretically predicted. They suggest that local micro- structural conditions such as the heterogeneous pre- cipitiation of carbides in austenitic steels, at the crack tip control the spread of plasticity.

8Hahn et al verified the existence of two distinct regions of plasticity surrounding a fatigue crack. Etch pitting techniques revealed a region of highly strained material adjacent to the crack, sharply delineated from a lightly strained region spreading further into the bulk of the material, indicating the presence of cyclic and monotonic plastic zones.

Dislocation structures that exist around propagating fatigue cracks have been the subject of investigation by a number of workers12 » 10 » 11 . The majority of this work has been carried out on f.c.c. materials where dislocation structures are found to exist as cell substructures and loops dependent upon AK, strain amplitude and stacking fault energy.

6

Other investigations5 have been carried out using resistivity techniques and metallographic studies involving linear analysis of the deformed material. Results suggested that plastic zone sizes and shapes are controlled by local microstructural conditions at the crack tip rather than stressintensity^range • Electron channeling contrast techniques have also been used to investigate cyclic deformation and subcell formation in fatigue crack propagation of a variety of materials13.

1.3 INTERMEDIATE RANGE FATIGUE CRACK GROWTH

1.3.1 MODELS

It is now widely recognised that fatigue crack growth rate, da/dN, can be related to the alternating stress intensity (AK = Kraax - Kmin) by the simple power law:-

where C and n are constants14 .

This equation gives an adequate, but not complete, description of behaviour for mid-range growth rates, (ie approximately 10” 6 - 1CT3 mm/cycle for air). At higher growth rates when Kmax approaches the fracture tough

ness, equation 10 underestimates the propagation rate15, whereas at lower growth rates it is found to be conservative as AK approaches the threshold AK, AKT^ , below which fatigue crack growth cannot be detected.(see Figure 8)

It has been suggested16 » 17 that at high growth rates the

factor

m - « AKi>n 10

final acceleration to instability occurs at some critical value of K and is consistent with the linkage ofIDclXindependently initiated facets. The model developed forpearlite/martensite structures suggested that as a fatiguecrack encountered a band of martensite a smaller plasticzone is produced, due to the higher yield stress, thetensile stress is therefore higher and the martensiteband cleaves. As K increases more cleavage takes placemaxand the uncleaved ligaments fail by tearing or accelerated fatigue crack growth and the static modes of failure become increasingly self sustaining.

Other models have also been produced involving static failure mode variables but taking into account cleavage failure modes18’ 19.

Robinson et al20, working on a titanium, found the fatiguefracture process involved the formation of faceted regions,primarily AK controlled, and their interconnection bylocal plastic tearing (primarily K controlled). Themaxmechanism was seen as a discontinuous process on a microscopic scale. Some grains, dependent upon their crystallographic orientation, fractured to produce faceted regions.

Crack growth by this faceting process will be restrained due to the presence of unbroken interconnected ligaments, and those ligaments will in turn be subjected to increasing stresses caused by the fracture of the surrounding material. It was suggested that any factor, such as low R ratio,

8

that increased the difficulty of attaining a sufficient tensile stress level to cause ligament failure would reduce the overall growth rate.

Knott21, 22 has suggested a model based upon the coalecence of microvoids formed around MnS inclusions (Figure 9). The mechanism proposed suggested that inclusions near a sharp crack are subject to increased strains. Voids form at low plastic strains because the MnS particles are bonded very poorly to the ferrite matrix. Void growth is limited until they are subjected to higher plastic strains and triaxial stresses which are concentrated in the region of the crack tip. The growth mechanism entails the growth of the crack, by an opening and blunting mode, and propagation to the nearest void.

Attempts have been made to describe region * C * fatigue crack growth where equation 10 is not applicable. Typical of these equations is23-

where A = A numerical constant which varies slightly with the material

Kc = Bacture toughness

which describes fatigue crack propagation as K approachesIDaXthe fracture toughness in pearlitic structures.

Others21* have proposed models based on the formation of striations, the work hardening of material ahead of the

da A AK4* 0 • 73 11dN max

9

crack tip25, the propagation rate as a function 6f loading parameters and material properties such as elastic modulus and cyclic yield stress:-

* £ = _ 12dN air E o Cp yc F

where a = A material constant having a value between 1 and 2E = Elastic modulus of the materiala = Cyclic yield stress of the material ycE-p, = A fracture strain term F

and da I K 2 - K2 . K 2 - K2 ^. „ / max m m T IC max=+8 I -------------- + In - 13dN K T 2 K 2 - K 2 .IC IC m m

where 8 is a material constant.

1.3.2 MECHANISMS

It has been widely reported26 that at low AK values,approaching threshold, and at high K values approachingmax

fatigue crack growth is sensitive to microstructure.The mechanism of growth in the intermediate fatigue crack

*growth range has been established by many workers16 , 27, 28as striation growth29 , 30 , 31 , 32 and the Paris equationis obeyed in this range16 , 33, 31 , 34. Research has shownthat each striation is produced by one cycle although every cycle does not necessarily produce one striation35.

Laird36 and others37 considered the production of ductile striations involves the alternate blunting and resharpening of the crack tip, as shown by Figure 13, and growth controlled by the local crack tip alternating plastic

10

deformation24 . Others have considered a shear decohesion model appropriate in this growth regime (see Figure 14).

McMillan and Pelloux37 proposed a plastic blunting mechanism for the production of striations which is supported by the data produced by other workers38. Striation spacings have been shown to correspond closely with macroscopic fatigue crack growth rates38 , 8 , however, ductile fracture modes and cleavage have been found to be associated with striations22.

Others39 have postulated that a transition from structure sensitive to structure insensitive growth occurs in the intermediate growth regime. Results indicated that the relationship between the plastic zone size and the grain size, or some controlling microstructural parameter, was a controlling factor in this transition.

Gerberich et al40 have shown that where combined ductile and brittle modes of fracture are observed then the constant, C, in the Paris relationship depends in a complex way on the stress intensity required to nucleate cleavage:-

where C = a constant dependent upon grain sizeK n u d " stress intensity required to nucleate

cleavage

da AK41 - 14

1 + 8/ir Sec"1 (K nucl

11

1.3.3 MEAN STRESS EFFECTS

1.3.3.1 INTRODUCTION

Whilst it has been shown that fatigue crack growth is insensitive to changes in mechanical parameters such as frequency, waveform41 and thickness42 early investigations on a number of materials43 have shown constants n and c in the Paris relationship may be influenced by intermediate fatigue crack growth rates44.

However, most investigations45, 34 , 46 have shown the effect of mean stress to be negligible in the intermediate fatigue crack growth range, growth being primarily dependant upon the alternating stress intensity where growth appears to be controlled by the amount of crack opening per cycle29 and is dependent upon the crack tip plasticity and ultimately on the elastic modulus30. A marked influence of mean stress has been observed at high fatigue crack growth rates approaching and also at growth rates approaching threshold (Figure 15).

Irving and Kurzfeld47 have shown for tests carried out in vacuum, on quenched and tempered steel, that no influence of mean stress is present at low values of AK, however, some influence is observed at higher values. In contrast, Ohta et al48, working on stainless steel found a influenceof R ratio at all values of AK.

A number of workers have indicated that the influence ofR ratio on fatigue crack propagation may be partly

12

explained by the mechanism of fracture. Investigations have shown that as the mean stress increases the proportion of cleavage increases and the overall propagation rate accelerates. Richie and Knott49 have found that provided the fracture mechanism was normal ductile propagation, producing striations, mean stress had no effect and growth depended on AK only and the occurrence of periods of either void coalescence or intergranular fracture lead to mean stress sensitivity.

A factor of ten difference in crack growth rates between R ratios of 0.34 and 0.85 has been reported44 in cold rolled mild steel; this was attributed to the presence of residual stresses introduced as a result of cold working.

Frost et al43 reported the influence of mean stress levels in an Al 5.5% Zn alloy to be attributable to the presence of hard intermetallic impurities in the alloy causing periods of fast fracture accompanying normal fatigue crack growth.

Static modes of failure have been reported by a number of workers45, 50 to account for R ratio effects, and in the absence of these static modes, growth rates are insensitive to mean stress levels.

Work on a high nitrogen steel51 tested near the ductile brittle transition temperature and a temper embrittled steel49 suggestedvthat cleavage 'bursts' occur at a critical value

13

of maximum stress intensity factor, K_IllaX

It has been shown for negative R ratio tests52 that the compression portion of the loading cycle does not significantly affect crack growth rates except when tensile residual stresses are present. It was also indicated that the transition from a ductile mode to the crackdirection to a shear type mode at 45° to the. propagation directions (see Figure 16) occurred at growth rates of 2 x 10“ 7 to 7.3 x 10“ 7 mm/cycle for all R values in aluminium alloy sheet, but is dependent upon thickness.

1.4 NEAR THRESHOLD CRACK GROWTH MODELS

A considerable amount of work has been carried out in recent years to determine the mode of failure and nature of near threshold fatigue crack growth. It has been suggested29 that facet formation observed in the threshold region may be the result of small scale reversed plasticity ie a mode of growth resembling stage I occurring

on a grain to grain basis. Although unlike stage I, cracks do not in general form on the primary slip plane it is clear from the large deviations out of the macroscopic crack growth plane that an element of shear mode growth is involved.

Other workers have produced dislocation models for fatigue crack growth at low stress intensities12, 53. Hornbogen et al12 proposed a dislocation model based upon the relationships between plastic zone sizes and grain sizes.The model is shown schematically in Figure 10. The cyclic

14

plastic zone is approximated by S-f, the static plastic zone size by 6S ~nd the grain size by D.

6 = 1 2 s 15

and

16

where a is the yield stress of the material, ys

When 5 „ < 6 < D. Dislocations are nucleated at the crackf stip and travel to the interior of the grain until the external stress has exceeded the yield stress.

When 6„ < D < 6 . Dislocations pile up at the grain boundary X sunder static stress and cross slip out of one plane becomes more likely than in the previous stage. The size of the pile up in this case is limited to the grain size.

When D < 6„ < 6 . As 5 is larger than 5- dislocations f s s & fare nucleated in two or more grains ahead of the moving crack. The size of the pile up is limited by the grain size; additional cross slip and nucleation of slip at grain boundaries.

Sadanada et al53 introduced a model based on the minimum AK required to cause the nucleation of a dislocation at the crack tip,

A ^ m in = 2ttpt17

cos 6 / 2 S'in 9/2 cos 0/2

15

where p = Distance between dislocation and crack.= Total stress necessary to nucleate and move a

dislocation from the crack tip.

9 = Crystallographic orientation of the slip system with respect to the crack plane.

The model suggested that the threshold AK is nearly independent of all material properties except elastic

modulus.

A number of workers have tried to relate the fatigue threshold AK to the R ratio.

Masounave and Bailon54 suggested a relationship of the form,

where AK is the stress intensity factor at R = 0. Thisrelationship predicts that. A K ^ is a linear function of R only. Other workers55 have suggested an adaption of this,

where y is a constant.

The data from a number of sources appears to fit an expression of this form.

Davenport and Brook56 have suggested that a simple power law relationship does not exist and proposed the expression

AKTh = aKq (1 - R) 18

AKTh “ W - R >Y 19

max (1 - R) 20

16

which predicts a decreasing threshold AK withincreasing R ratio. This equation can be approximated tothe Klesnil and Lukas relationship55 with exponent 0.33when K „ is equal to AKm, , x and has been demonstrated max ^ Th (o )to be appropriate to 0.15% C 1.5% Mn steels.

A model proposed by Schmidt and Paris168 related the crack closure phenomena to load ratio effects at the threshold:-

for low load ratio:- AKmu = K - K . = K ( 1 - R )Th max m m max - 21

=

AKc ^ = Minimum value of A K ^

and has been applied to low alloy steels57.

A simple model proposed by Masounave et al55 to explain the grain size effect produced in the near, threshold region is based on the microscopic crack path morphology. This model is also the basis of one produced by Priddle59. Near threshold facture surfaces are characterised by considerable zig-zag deviations of the fatigue crack from the plane normal to the principal stress. The magnitude of the deviations is greater in coarse grained material than in fine (Figure 11). Fracture mechanics theory applies to a crack which is assumed to grow perpendicular to the principal stress. In practice the AK value is lower than that predicted from the stress intensity calibration. Crack deviation away from the plane of maximum tensile stress leads to a reduction in and and increase in stress intensity components (Figure12). Further reduction in AK arises due to an increase in the real crack surface area compared to that obtained from macroscopic measurements.

Modelling crack growth, particularly near the threshold is difficult since the influence of microstructure on mode I/mode II growth must be considered. It is even more complex if the crack is advancing in a discontinuous manner, held up at various points along its leading edge by microstructural obstacles. McEvily60 has proposed a model where growth is related to the crack opening displacement with a modification to take into account

18

the contributions of static modes of separation in the growth process,

a = Yield Stress ysE = Youngs ModulusA = A material constant depending upon material and

environmentK = Fracture Toughness c

Others61 , 62 have attempted to include a component to take into account crack closure effects (see Section 1.5.3.7) on the unloading part of fatigue cycle. This has leadto the formation of further equations

— = C 1 (AK ,,)ml - 26dN eff'

where AKgff is the effective AK and is equalto K - K opening, max

daThe relationship between and K ^ has been shown to be linear for low carbon steels61.

Tanaka63 has proposed an empirical relationship taking into account microstructure , material strength, fracture toughness and specimen thickness, for ductile steels in the intermediate to threshold range

Th (R )max

Th (R )

24

25

19

dadN = 1.700 x 10-4(AK/103.6)m - 106 - 27

and

AKTh = 163.6(5.88 x 10 3)1/,m - 28

Other relationships have been determined for brittle steels Petit and co workers64 have proposed a relationship which describes crack propagation from the threshold to intermediate rate and include an environmental constant.

da— = e(R; ct) dN

1 - KThKmax /

KmaxKTh

m

- 29

where m is a constant depending upon the environment.

Further models attempt to include terms describing the critical crack root radius, the strain distribution and the plastic zone size:-

AKTh = E pm m

where p . = Critical crack root radiusm mE = Youngs Modulus

= Real fracture strain.

1.5 FATIGUE THRESHOLDS

- 30

1.5.1 INTRODUCTION

Little is currently known about the micromechanisms of fatigue crack progagation at near threshold growth rates.It is important from a design point of view that engineering

20

and metallurgical data of this type is provided to allow design of components and materials65, capable of withstanding high frequency low amplitude loading for lifetimes up to 1012 cycles.

Most studies of fatigue crack propagation have confirmed that the crack growth rate da/dN is a function of the alternating stress intensity AK through the power law expression,

da/dN = C(AK)n - 10

The expression, however, overestimates the growth rate as AK approaches AK,^.

It is well established17, 33, 66 that a threshold for fatigue crack propagation does exist. However, the exact nature of this threshold has yet to be adequately described. The micromechanisms of low growth rate fatigueare complex and a study of the literature67 indicates that

ojck— feat least 10 different propagation modes/voccur. Otherthan metallurgical variables there are a number offactors which may lead to an increase in thresholdcrack tip blunting, bifurcation, closure and residualstresses.

1.5.2 MEAN STRESS EFFECTS

1.5.2.1 INTRODUCTION

The influence of mean stress is often expressed in termsof load ratio, R, (= K . /K ), while, it is known that ’ * v m m ' m a x "

21

there is little influence of load ratio in the mid-range, growth rates near the threshold have been identified as being sensitive to load ratio (Figure 17)

It has been widely reported65-76 that decreasing the load ratio, increasing grain size20 and increasing the inter- sititial alloying content all produce significant reductions in fatigue crack propagation rates at low AK.

Cooke et al17 noted that the threshold fatigue crackgrowth behaviour was dominated by the R ratio such thatK rather than AK controlled the kinetics; K at the max maxthreshold remained relatively constant over the range ofR values. Others have observed K control on thresholdmaxvalues up to specific values above which threshold values tended to be AK controlled.

Richie found the increaseddependence of A K ^ on strength12 was less marked at high R ratios (Figure 18). McEvily et al77 working on Ti-6A1-4V has found reasonable comparison of results with an expression of the form,

KTh

where Km, , N is the threshold at R = 0 Th(o)

Many other attempts have been made to relate the threshold AK to mean stress, one by Radhakrishnan78 appears to fit experimental data for steels and aluminium alloys:-

1 - R Kr1 + R Th(o) - 31

22

log (AK)Th = I - + 1.14j + 0.7 log( 1 - R) - 32

where n is a constant.

The load ratio dependence on near threshold growth, however, is found to be lower with increasing temperature68 and inert environments37 , 1+6 , 77 .

Experiments carried out on En 24 and Ti-6A1-4V in'.vacuum46 indicated that near threshold crack propagation rates and the value of A K ^ were completely independent of loadratio. This lack of R dependence for tests in inertconditions has been confirmed for low alloy martensitic steels tested in vacuum47.

Other studies of Ti-6A1-4V show that for tests in vacuumthe dependence of the threshold on mean stress is markedly reduced though not eliminated79 the value of the threshold was significantly higher than in air.

These results indicate that the effect of load ratio on near threshold fatigue crack propagation rate may be attributed, in part, to some environmental interaction.The lack of load ratio effect on higher, mid-range growth rates is consistent with this since the environment may be unable to keep pace with the crack velocity.

More recent explanations of the load ratio effect havecentred around the phenomenon of crack closure68-70 which suggests that as the R ratio is decreased then a value of R is reached where the crack closes as the minimumof the stress cycle is approached. The crack closure,

23

occuiring at positive loads above Km^n > reduces the effective AK applied and therefore produces a higher value of AK,^

1.5.3 MICROSTRUCTURAL FACTORS

1. 5.3.1 MATERIAL STRENGTH

Investigations have indicated that fatigue crack propagation in metals is largely independent of yield strength67 and Lindley and Richards have found that raising the strength level by an order of magnitude does not affect the crack growth rate, over the mid-range, by more than a factor of two or three80.

The effect of material strength on intermediate growth rates has been investigated by Dowse and Richards81, working on low alloy steel weldments. They observed a marked reduction of crack propagation rate when a crack reached the hardened heat affected zone of the weld and considered this to be due to a reduction in the plastic zone size. No difference in crack propagation mechanism was observed between parent metal and heat affected zone.

However, at near threshold levels, material strength has been observed to have a large effect on the value of the threshold, A K ^ 79 (see Figures 18, 19). In low strength ferrite-pearlite steels, values of threshold have been observed to decrease significantly with increasing strength58 , 176 , 82. A large effect has been observed for high strength martensitic steels where the controlling measure of strength was the cyclic rather

than the monotonic yield strength29 . Coarse grained precipitation hardened ferritic microstructures significantly lower growth rates near the threshold and have a more pronounced effect than higher strength bainitic or martensitic structures83. The effects of yield strength on have been summarised for a number ofsteels (see Figure 20).

The effect of strength on near-threshold crack propagation behaviour is significantly less at high R values29.Varying the strength in low strength steels may involve variations in the ferrite grain size which also has a strong effect on near-threshold behaviour58, 19 , 34.

The effect of tempering temperature has been investigated for a low alloy steel85 and a peak value of threshold AK obtained as a function of tempering temperature (as the tempering temperature is raised then the U.T.S and the yield strength decrease continuously) (see Fig:ure 21).The threshold is then dependent on strength level on one side of the maxima and a characteristic material parameter on the other. Therefore suitable combination is required to give the optimum threshold value. Results showed that a coarse grain size and lath martensite gives inferior thresholds compared with a mixture of plate martensite and lath martensite formed in finer grained material.

The dependence of A K ^ on strength may be due to a number of factors,such as - larger plastic zones in lower strength material may retard crack growth.

25

Alternatively higher strength steels may be more susceptible to the effects of hydrogen, due to higher equilibrium solubility of hydrogen.

1.5.3.2 GRAIN SIZE EFFECTS AND CRACK TIP PLASTICITY

1.5.3.2.1 INTRODUCTION

It has been shown that grain refining can be beneficial in raising the fatigue limit or the endurance strength of materials86. Most studies at intermediate growth rates have shown that grain size has little effect. However, a number of studies on titanium alloys and steels indicate that a grain size effect is present at higher growth rates 67 (see Figure 22).

At very low growth rates an effect has also been shown to exist. Several workers57, 29, 87, 88 have observed an improved resistance to near threshold propagation with an increase in grain size (see Figure 23).

A number of investigators89 have reported a linear relationship between threshold and grain size, whilst others58, 61 have shown the threshold value to vary linearly with the square root of the grain size.

Robinson and Beevers20 have reported an order of magnitude decrease in near threshold growth rates in a Titanium after coarsening the grain size from 20 to 200 ym. Similar effects have been observed in Ti-6A1-4V. A marked increase in threshold AK values has also been observed in a range of low strength steels by increasing the ferrite grain

26

size, 58, 98 , 76. In these studies material strength was not controlled and the effect of grain coarsening may have been masked by a decrease in material strength.

Comparisons of threshold stress intensity values as a function of grain size, at constant yield strength, have been made in high strength steels29 , 30 , 72 and it has been determined that coarsening the prior austenite grain size by an order of magnitude led to a decrease in near threshold growth rate but left the threshold value unchanged; further data on low strength steels indicated a strong grain size affect on the normalised threshold13.

An increase in the threshold of duplex structures withan increase in the grain size has been attributed to adecrease in notch sensitivity with a decrease in strength level. It was shown26 that the martensitic phase was a barrier to crack growth and a crack could only propagate if the plastic zone size exceeded the size of the martensitic phase.

Masounave and Bailon18 have shown a linear relationshipto exist between the threshold stress intensity

iand the grain size d 2(Figure 24) and produced an expression relating A K ^ to d^.

AKTh = (1 ” R) (AKo + K fd4) ” 3

where AK = Threshold when R = 0o= Factor dependent upon the local stress ahead

of the crack.27

The threshold AK has also been shown to vary linearly with the monotonic yield stress89 and the mean stress79. Thompson90 has suggested that the influence of grain size on fatigue, in a low carbon steel, may be correlated with the ease of cross slip of the system.

In contrast to other workers Robin et al91 found no significant effect of grain size on the fatigue threshold, in aluminium alloy. Fracture surfaces consisted of flat facets separated by steps, the facets being approximately equal to the grain size. They determined that the relationship between the grain size and the plastic zone size was not significant in the transition from crystallpgraphic type growth to non-crystalographic growth. Transition occurred at a constant growth rate independent of grain size.

Q OHigo et al , working on Cu-Al alloys, have noted a regular increase in fatigue crack threshold with d” ̂which becomes more pronounces as the stacking fault energy is decreased (see Figure 25). The fatigue fracture surfaces showed a high proportion of intergran- ular facets at low AK levels. -Their explanation suggested that a process depending on reversed dislocation movement at the crack tip was a function of the alternating plastic strain amplitude. Lower strains would be developed in higher yield strength material for a given AK; if a critical value of alternating plastic strain amplitude, Asp, were required to produce crack

28

growth then this would require a higher AK so that an increase of A K ^ with yield stress would be expected.

If a constant reversed plastic zone size were required to propagate a crack then A K ^ would vary in a linear manner with yield stress.

1.5.3.2.2 PLASTICITY EFFECTS

It has been observed by many workers29 that the threshold condition is achieved when the reversed plastic zone size is of the order of the grain size.

Robinson et al20 have noted the occurrence of grain orientation control when the reversed plastic zone size was approximately equal to the grain size.

Others33 have shown that as the reversed plastic zone size exceeds the scale of the microstructure a growth mode occurs which is insensitive to microstructure, R ratio, and to a large extent environment. Where the reverse plastic zone size is smaller than the scale of the microstructure, stage I type growth occurs and this process tends to be Kmax rather than AK dependant.

A number of workers61 , 67 have reported the transition from structure insensitive growth to structure sensitive growth to occur when the reversed plastic zone size was of the order of the grain size. The dislocation structure ahead of a crack and the effect of a change in grain size is schematically shown by Lindigkeit et al93, 95 in Figure 26.

29

Taira et al61 working on low carbon steel, showed that theratio of the reversed plastic zone size, W v ,to thegrain size, d, to be of the order of 1.5 - 2 . Theyproposed that the threshold condition is determined by whether the slip band near the crack tip propagated into an adjacent grain or not, and that the slip band propagation wasgoverned by the AK at the slip band tip. It was suggestedthat the microscopic K could be approximated by:-

Gerberich et al67 suggest that although the R.P.Z.S mightbe fundamental to the transition from microstructuresensitive to microstructure insensitive growth near thethreshold, this zone was an order of magnitude smallerthat the controlling microstructural parameter in Ti-6A1-4V. They also reported a poor correlation between theR.P.Z.S and AKmu in steel.Th

These workers indicated that at the threshold, the stress distributions associated with the crack, which is a

Km = K - K_p * fr 33

34

and afr* = stress in the slip zone

= size of the slip band zone in the forwarddirection

and thus K = Km + 2 J T afr* J ^/tt 35

and at the threshold

KTh = K” CVH + 2 cfr* '/p2s/" 36

semi-cohesive zone associated with the selective cleavage of the microstructure and the plastic zone, must be in equilibrium. An expression was derived for a central crack length 2c in an infinite plate:-

ttcj - 2a Cos"1 |- 1 - 2(a - a ) Cos"1 (~ )= 0 - 3'sc \ a J ys sc7 \ ay

where a = Applied stressa = Stress in semi-cohesive zonesca = Yield stress in plastic zone ys ^2c = Real crack size2b = Real crack + semi-cohesive zone size2a = Fictitious crack containing all three zones

The agreement with experimental results from a number of sources was reasonable, (see Figure 27).

1.5.3.3 EFFECT OF GRAIN BOUNDARY SEGREGATION

It is well known that grain boundary segregation can severely impair toughness of low alloy steels (temper embrittlement).

A study has been conducted72 on the effects of impurity segregation on near threshold fatigue crack propagation, in an ultra high strength steel. (Tests were conductedat the same grain size and yield stress). It wasdetermined that no difference in propagation rates was observed between the unembrittled and embrittled structures at mid-range growth rates. At near threshold levels, impurity induced embrittlement gave rise to vastly accelerated growth rates and a corresponding reduction in

31

aK,^ at both high and low R ratios.

This effect was accompanied by a significant increase in the proportion of intergranular fracture in the embrittled steel close to the threshold. This effect at low growth rates compares to little or no effect at intermediate rates.

1.5.3.4 EFFECT OF MATERIAL PURITY

It has been observed that crack propagation rates are considerably enhanced by the presence of impurities in steel (see Figure 28). Evans et al94, working on En 24, showed a threefold decrease in propagation rates in high purity alloys compared with a standard commercial alloy, at near threshold AK.

Differences in growth rates were most apparent in the Paris regime; the growth data tending to converge near the threshold. Less convergence of data was observed in tests carried out in vacuum, however, differences in tempering temperature were also shown to affect growth rates.

1.5.3.5 MICROSTRUCTURE AND MECHANISMS

The importance of microstructural parameters in very low growth rate fatigue has been the subject of study by a number of workers and it is known that changes in the microstructure in,for example,weldments,95 can lead to a considerable difference in growth rates. A decrease in the interlamellar spacing, in the absence of ferrite matrix hardening, increases the threshold values for

32

fatigue crack propagation, in pearlitic steels96 .

Although it has been widely reported24 that near threshold fatigue crack propagation is sensitive to microstructure, the precise mechanisms are not known. Macroscopically a band of corrosion product is generally observed on fracture surfaces in the area where growth rates have been less than 10~6 - 10”7 mm/cycle17, 46, 74. This indicates the presence of environmental action at near threshold levels even in air.

Microscopically, near threshold growth has been termedmicrostructurally sensitive24, 27, 17, 37, 46 owing to thepresence of isolated planar, transgranular or intergranularfacets within a flat, ductile transgranular mode17.Secondary cracking and rough steps may also be presentand may be indicative of environmentally sensitivefracture. The dependence of intergranular fracture onAK and K at threshold is shown in Figure 29.nicix

Work on iron carbon alloys31 determined that failure at low growth rates was preceeded by intergranular separation of ferrite grains. Slip lines across these grains indicated that slip has occurred within them after the passage of the crack tip. These features were observed to occur when the reversed plastic zone size was approximately equal to the grain size.

The appearance of isolated intergranular facets46 in addition to ductile striations has been observed by a number of workers49. It has been shown that rates of

33

growth in the near threshold region vary depending on the type of microstructure present. Fracture surfaces have been observed to be very irregular in appearance and contain many deviations from the primary fracture plane20. This scale of irregularity was found to increase with the scale of the microstructure, in agreement with the model proposed by Masounave et al58. The mechanism for the formation of these facets in the threshold region is thought to be the result of small scale plasticity, a pseudo stage I mode of growth occurring on a grain to grain basis.

Further investigations suggest that these facets, unlike stage I cracks, do not in general form on the primary slip plane; but is is clear from the deviations that an element of shear is involved.

Irving et al9 suggested that the formation of fracture facets was aided by shear modes of failure rather than tensile mode I (Figure 12) which operates once the transition to structure insensitive growth has occurred. They conclude that structure sensitive growth consisted of facet formation in a pseudo stage I shear mechanism, coupled with an environmentally assisted failure of the intervening regions. It was proposed that a two stage mechanism existed; one part AK controlled (the formation of facetsat and ahead of the crack tip) and the other K^ ' maxcontrolled (the inter-connection of these facets).

Experiments on ultra high strength steel29 determined that fracture consisted of a flat transgranular mode

34

with isolated segments of intergranular separation. Others have shown that fracture path topography is strongly sensitive to the orientation of the grains through which the crack front passed.

The threshold condition for microscopic fatigue cracks in two phase microstructures, for example martensite/ferrite, has been shown to be controlled by the martensite phase, and a crack growth resistance term represents amaterial characteristic. Smaller values of AKi compared with KTk(m ), will produce non propagating cracks in the matrix. A further observation suggested that the crack front near the threshold is moving in a discontinuous manner with the front being held up at various points by microstructural obstacles (second phase particles, ligaments or improperly oriented colonies of grains).

The presence of static modes of failure during fatigue at low growth rates has been seen to be as a result of restricted slip systems34, embrittlement and environmental influences and it is known that control of the microstructure can lead to an improvement in threshold behaviour26.

Gerberich et al67 considered a mixed mode of fracture at near threshold growth rates where cleavage occurs in large grains but not in some of the smaller ones. The resulting ligament acts as a traction on the crack preventing opening, thus reducing the AK at the crack tip. Alternatively fracture may occur in those grains which are most favourably orientated and those which are

35

unfavourably orientated remain as ligaments.

The dynamics of ligament fracture and static discontinuous fracture modes are among a number of variables which may influence very low crack growth rates; others may be crack blunting, crack branching and void formation.

1.5.3.6 THE BEHAVIOUR OF DISLOCATIONS

1.5.3.6.1 INTRODUCTION

It has been known for many years that dislocations play a significant part in the conditions for crack growth98 and theories of their role are well developed99 , 10 0 , 10 1 .

Work in the early 1960's102 on fatigue induced dislocation sub-structures in poly-crystaliine aluminium showed even at low.strains, large concentrations of dislocation loops were found in the vicinity of sub-grain boundaries.

Recent investigations have indicated the presence of dislocation tangles103 and cell sub-structures104, 105 adjacent to the crack tip. Katagiri et al103 have noted in addition to a high density of dislocation tangles a change in sub-structure on lines radiating from the crack tip at 60° to the direction of crack growth. They suggested that the slip band/dislocation structure indicated a complex strain distribution occurring near lines of discontinuity in cryst&Hographic orientation.Intense plastic flow was observed at the tip of the crack along the planes close to the plane of maximum elastic shear stress.

36

A number of models have assumed that crack growth is facilitated by the nucleation and motion of dislocations at the crack tip. It therefore follows that easier nucleation of dislocations enables crack growth to occur at lower aK lwith less crack tip blunting.

1.5.3.7 CRACK CLOSURE CONCEPTS

Recent theories of fatigue crack growth, particularly in the threshold region, have suggested an effect of crack closure106 on threshold values.

It has been postulated that as the R ratio is decreased then a value of R is eventually reached where the crack begins to close as the minimum stress intensity of the load is approached. Crack closure reduces the effective AK applied to the specimen and so has the effect of raising the apparent threshold stress intensity measured for a given R ratio.

If closure does not occur then the R dependence of AK,^ disappears.

Alternatively the R ratio effect could be caused by the formation of oxide which acts to hold the crack open at low R ratios leading to a reduction of the effective AK applied to the crack and a consequent rise in the apparent AK^. This would also account for the lack of any effect in vacuum.

Work on fully pearlitic steels at low R values107 has indicated the presence of oxide on the fracture surface

37

along with an increase in the surface roughness withincreasing grain size. It is suggested that the residualplastic deformation present along the path of a growingcrack leads to some closure of the crack surfacesat positive values of K . . This leads to an effectivem mreduction of AK (ie A K ^ ^ < AK apparent) which is available to act as a crack driving force. At higher R values the crack remains open during the whole of the loading cycle and the role of crack closure disappears.

In oxidising conditions, closure could lead to enhanced corrosion debris formation within the crack tip region by repeated breaking and compacting of the oxide. This could cause increased contact between the crack surfaces thereby decreasing A K ^ ^ and reducing the crack driving force. It was suggested that the effect of a finer grain size was to reduce roughness. The appearance of a mismatch of striation peaks has also been shown to lead to closure.

Further work on medium strength steels108, aluminium alloys109, titanium110 , and nimonic alloys111 has shown a dependence of crack growth rate, at near threshold values, on crack closure occurring at low R ratios.

The magnitude of the closure effect has been estimated using the equation:-

where a^s = The yield strength

E = Youngs Modulus6 = Crack opening displacement

This equation has been found to fit well with the size of oxide particles at the crack tip

The closure phenomena may also be used to explain the effect of strength level on threshold. In higher strength steels, smaller plastic zones are formed ahead of the crack and therefore closure effects will be reduced, giving rise to lower AK threshold values, particularly at high stress ratios. If crack closure effects are reduced, then the amount of fretting corrosion products might also be expected to be reduced. The effective stress intensity range of the higher strength material will be closer to the applied AK giving higher crack growth rates, and lower threshold values.

1.5.4 ENVIRONMENTAL ASPECTS OF FATIGUE CRACK GROWTH

1.5.4.1 INTRODUCTION

It has been observed20, 33 that the stress intensity range, AK, required for crack growth in vacuum is very much greater than that required for air (Figure 30). It is therefore important that a complete understanding of the environmental effects in fatigue crack growth be obtained to enable the design engineer to evaluate requirements of components for service in other than vacuum conditions.

39

1.5.4.2 INFLUENCE OF MICROSTRUCTURE

Observations suggest that environments play an active role at low growth rates20, 46, 112. Many workers47, 113 , 114 have found large differences46, 115, 116 in near threshold growth rates between hydrogen containing environments and vacuum (see Figure 31). Extensive tests carried out in other environments (sea-water117 , Nitrogen115, 3% NaCl57) have also shown considerable differences.

In the intermediate growth range most workers have found little influence of environment119 , although some workers have noted an influence in this range113, 91 . An increase in crack growth rates by up to a factor of 8 has been observed in aqueous solutions and a critical frequency wasdetermined at which maximum environmental attack occurred120 #

In vacuum little detectable influence of R ratio on growth is observed at low AK values47. Research also suggests that there is little influence of water vapour on growth rates less than 10“ 5 mm/cycle in quenched and tempered steels. However, at higher AK values some influence of R ratio was apparent. Stewart115 has suggested that the growth rate in an environmental species can be expressed by a simple relationship of the form:-

Total mech 39

where f is the frequency of testing.

40

Reports suggest that a t !low AK values, growth becomesincreasingly sensitive to K and under these conditions & * maxthe influence of environment becomes more marked and non-continuum mechanisms - cleavage, intergranular fracture and void coalescence become operative.

Frandsen et al8, observed a transition in failure mode from ductile transgranular fracture in vacuum to a mixed intergranular and transgranular mode in hydrogen. A correlation was shown to exist between the increase in crack propagation rate caused by hydrogen and the proportion of intergranular fracture (Figure 32). The maxima correspond to the point where the forward yield plastic zone size is equal to the prior austenite grain size.

The appearance of the fracture surfaces at low growth rates has indicated that cracking mode changes from ductile to 'quasi cleavage'94 and is consistent with a hydrogen related embrittlement mechanism 114, growth showing a time and maximum stress dependence analogous to stress corrosion cracking, the change in the fracture mode being associated with hydrogen enhancement of fatigue crack growth121 .

Stewart79 , working on two low alloy steels found little influence of environment (hydrogen) at stress intensities close to the threshold and noted that these results were inconsistent with the hypothesis that the effect of strength level and stress ratio on the threshold is as a result of hydrogen embrittlement. He further suggested that the build-up of corrosion products within

the crack by fretting in moist environments also has a marked effect on A K ^ values at low stress intensities.

Work on Cu-Al alloys92 suggested that the occurrence of intergranular cracking could be associated with preferential oxidation effects at the crack tip. At low crack growth rates more time is. available for preferential oxidation to occur along grain boundaries adjacent to the crack tip. At higher growth rates cracks will propagate more rapidly than oxidation down grain boundaries could occur, and the incidence of intergranular facet formation would fall.

1.5.4.3 MECHANISMS OF CRACK GROWTH IN ENVIRONMENTS

It has been proposed that the microstructural effects observed at near threshold stress intensities (for tests carried out in moist air29) could be due to the presence of hydrogen, a semi-qualitative model relating the contribution to fatigue crack propagation from the environmental effect of hydrogen, evolved from the crack tip surface reactions with moist air was proposed. It was also suggested that the observations of lower growth rates in coarser grained material will be due to the diffusion of hydrogen atoms to grain boundaries, ie - transport of hydrogen from crack surface into the metal through the motion of dislocations122, 123 rather than diffusion121. However, the dumping and pickup of H 2 at the grain boundaries has been shown to be a fast process and is not rate limiting122-123.

42

Investigators considered that hydrogen was transported on dislocations in Cottrell type atmospheres124. The presence of an atmosphere around a dislocation, however, may cause a drag on the dislocation thus reducing their mobility. The hydrogen may then be deposited at micro- structural locations such as grain boundaries, inclusions or microvoids. These locations may then be the critical paths for fracture.

It was further suggested125 that since the dislocations are unable to travel from grain to grain, hydrogen carrying dislocations which approach grain boundaries will deposit their hydrogen at or near the grain boundaries where the hydrogen atoms are picked up by mobile dislocations emitted from sources in the adjoining grain. It is therefore possible for dislocations to transport hydrogen deep into the plastic zone even at ambient temperature125.

The concentration of hydrogen atoms reacting at the grain boundaries was thought to be greatest when the maximum plastic zone size is of the order of the grain size. In coarser grained structures the plastic zone size remains small compared to the grain size until much higher stress intensities resulting in a reduced environmental influence.

The formation of microvoids ahead of the crack tip has been observed in ferrite126 and the segregation of hydrogen to the grain boundaries contributes to the formation of cracks. The observance of the formation of secondary cracks in the elastic-plastic zone head of the crack tip

43

and their coalescence with the primary crack84 leads to the suggestion that crack propagation would only occur when the local stress127 exceeds that required to break the Fe-H-Fe bond. The threshold is then a function of this local critical stress.

Comparison of fatigue crack propagation data in air and vacuum, for nickel based alloys128, indicated that a higher and more clearly defined threshold occurred in vacuum; it was proposed that crack blunting resulted in a rapid approach to a clearly defined threshold. Fatigue crack propagation was observed to be reduced by slip reversal. The effect of environment was to retard slip reversal by oxide pinning of the dislocations. Oxidation also reduced rewelding of the crack surfaces on unloading.

A model proposed by Lynch129 suggested that surface lattice distortion could hinder the nucleation and ingress of dislocations at the surface since dislocations moving in the first few atomic layers would be associated with larger than normal lattice distortions. The effect of an environmental species present at the crack tip would be to increase the number of neighbouring atoms, through chemisorption, and reduce the surface lattice distortion, thus facilitating dislocation activity at the crack tip. The model indicated that chemisorption of environments (liquid metals, aqueous, moist air etc) could therefore be responsible for enhanced growth rates. The effect of frequency can be explained on the basis of the effectiveness of the environment in promoting crack growth and

is a time dependent process. .

At higher crack growth rates the environmental effects would be expected to disappear, as indicated by a marked reduction in the proportion of fracture occurring by an intergranular mechanism. At high cyclic frequencies the hydrogen atoms will no longer be able to diffuse sufficiently rapidly to keep pace with a crack tip which is advancing at a high rate.

Recent investigations have focused on the phenomena of crack closure and the part played by environmental species at low growth rates. This is more fully discussed in section 1.5.3.7.

1.5.4.4 KINETICS OF HYDROGEN EFFECT

Investigations have suggested that the kinetics of the environmental effect are controlled by the diffusion of hydrogen to the crack tip, dissociation to atomic hydrogen at the clean metal surface adsorption into the metal matrix and finally diffusion through the lattice to the region of embrittlement. The rate limiting step is variously thought to be the surface processes130 and the long range diffusion of hydrogen131 .

Others have suggested that the controlling mechanism may be a critical concentration of hydrogen, ie the applied stress intensity equals the threshold when the equilibrium concentration of hydrogen at the crack tip achieves a critical concentration.

45

1.6 THE FATIGUE CRACK GROWTH OF SILICON IRON

1.6.1 INTRODUCTION

Research on the fatigue crack growth of silicon iron, particularly in the threshold region, is not common. However, as a single phase system it is ideally suited to threshold work and investigations into restricted slip systems.

The addition of silicon to iron produces solute strengthening making it increasingly difficult for cross slip to occur and restricting plastic deformation within the grains. It has been reported18 that additions of silicon to iron increase crack propagation rates, Figure 33, and also result in an increasing proportion of cleavage (silicon decreasing the fracture stress) and that a change from intergranular to transgranular propagation is observed132.

The intensive slip band formation which is characteristic of other materials in cyclic deformation has not been observed in silicon iron193 . Others have reported134, 135 that dislocations tend to remain on the (110) plane rather than cross slip readily on to other types of plane as in pure iron. This leads to an increase of fatigue resistance, however this improvement cannot be ascribed solely to the increased resistance to cross slip because the yield stress of iron is also increased by the addition of silicon, although other workers report that the yield stress has little effect on threshold levels of silicon iron67.

46

Earlier work on Fe-Si single crystals136 t 137 indicated that cyclic cleavage is initiated by an increase in the rate of loading138 . Further investigations139 on the system have shown that the crack tip opening rate is the controlling factor in determining whether a crack propagates by a ductile or brittle mode. The critical crack opening rate at which the fracture mode changes is temperature dependent and an activation energy for the initiation of cleavage has been determined. The activation energy for dislocation glide agrees well with the activation energy for the transition from ductile to cleavage fracture.

Gerberich et al140 have proposed a cyclic cleavage crack growth model based on that of Neumann139 for crack growth in iron and some of its alloys. It was shown that a decrease of a factor of five in crack growth rate occurred on a reduction of temperature from R.T to 233 K in an iron 2% silicon alloy. The yield stress was shown to increase from 199 to 222 MPa over this range of temperature but it seems improbable that such a small increase in yield stress could have such a large effect on the growth rate.

At lower temperatures they reported a further increase in yield stress from 222 to 370 MPa, however this did not reduce the growth rate as might be expected. The cleavage mode became predominant and the trend in growth rates was reversed.

Similar behaviour was noted for Fe 2.5% Ni alloy where

47

growth rates were shown to increase by almost a factor of 30 as the temperature falls to 173 K which corresponds to an increase in yield strength 160 to 240 MPa.

Gerberich et al67 noted that a 1% silicon addition to iron decreased the ductile/brittle transition temperature slightly while greater amounts of-silicon increase it.Small additions of silicon produced solute softening and therefore the yield stress is actually lower than the pure iron at 173°K.

Neumann et al141 stated that alternating activ ation of two intersecting slip planes results in crack growth and showed that in’quasi-britt le ' crack propagation in Fe-3% Si the activation energy for brittle crack initiation was equal to the activation energy of dislocation motion.

The low cycle fatigue of Cu-Al polycrystalline materials has been shown to produce ’cell substructures’ ahead of the fatigue crack. Dislocation 'bands’ and 'tangles' were observed parallel to the primary slip planes which is indicative of the planar dislocation arrays encountered in low stacking fault energy material. Dislocation bands occurred at all strain ranges; slip band coarsening occurred as the strain level was increased.

Recent work on grain orientated silicon iron143 has suggested that the appearance of cleavage facets on the fatigue fracture surface is associated with inhomogeneous deformation along the crack front. Results indicated a reverse plastic displacement, 6D , almost two orders ofK

48

magnitude larger than the growth rate and suggested that the occurence of crack closure provided a possible explanation.

Further work on similar material11*4 indicated that crack growth occurred by means of slip occurring at the apex of the crack tip; slip of upper and lower slip planes formed new surfaces at the crack tip during the loading cycle, crack closure occurred by means of reverse slip at the apex during the unloading cycle. The deformation cycle was found to coincide with the slip directions of the material and deformation in the reverse direction was found during the unloading cycle.

49

2 EXPERIMENTAL PROCEDURES

2.1 MATERIALS

High purity Japanese electrolytically refined iron melted in a Scotvac vacuum furnace under an atmosphere of argon together with small quantities of silicon was used to obtain the desired composition. Initially twelve 5 kg ingots were produced with silicon contents varying from 0 to 4%.

A further series of four ingots were subsequently produced containing small quantities of aluminium and nitrogen. It was hoped to produce a fine dispersion of aluminium nitrides in order to produce a degree of grain boundary pinning and retardation of grain growth.

A third series of eight ingots was produced to supplement the first in the mechanical working and heat treatment experiments.

2.1.1 CHEMICAL COMPOSITION

Tables 1, 2 and 3 show the chemical composition of the three series of material respectively. Analysis was determined using a combination of wet and X-ray analytical techniques on samples representative of the melt. The analysis of base materials is given in Table 4 and the analysis of residual and tramp elements for series 3 material is given in Table 5.

50

2.1.2 MECHANICAL WORKING AND HEAT TREATMENTS

The cast ingots, of initial dimensions approximately 230 x 60 x 60 mm, were cropped (to remove pipe) and skimmed to produce a surface suitable for rolling.

Conditions of plane strain at the crack tip are necessary to achieve a. uniform crack front shape during propagation.It is known that under plane strain conditions, fatigue cracks tunnel ahead more rapidly than under plane stress conditions likely to be found at specimen surfaces. Only a small reduction was possible due to the constraint on specimen size and therefore little effect of orientation might be expected.

The cast structure in all cases was very coarse, the central sections of the ingots being coarse equiaxed grains up to 4 mm in diameter surrounded by columnar grains up to 20 mm in length.

Initial hot rolling treatments from 1000°C to a finished rolling temperature of 800°C were made to ingots ISOOB,IS20B, IS30A, IS40A. Initially ingots were rolled with the maximum pass permitted by the mill (up to 13%).These treatments failed to produce the desired equiaxed grain structure. A final grain size of 2.6 mm was achieved in the case of ingot ISOOB. The cast structure of ingot IS20B was only partially broken up by the treatment and little break up of the cast structure was

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observed for ingots 1S30A and 1S40A.

The results of these experiments indicated the necessity for a cold or warm working treatment. An attempt to roll ingot 1S05B was made using the smallest available pass (= 0.5%). This resulted in extensive cracking of the ingot surface, up to 5 mm deep.

Ingot 1S20A was hot rolled at 1050°C to 30 mm in thickness and a final 5 mm cold reduction to introduce sufficient strain energy to facilitate a grain refining heat treatment utilising this strain energy. Extensive cracking of the billet occurred on the first pass of 7% rendering the billet unusable. The cracking was identified as grain boundary decohesion.

Ingot 1S10B was rolled at 800°C employing passes of 2%. Cracking started to occur on the third pass and the experiment was terminated. The cracks were subsequently removed and the ingot re-rolled at 1000°C down to 30 mm and the final 5 mm rolled at 800°C. Again grain boundary decohesion occurred at small passes.

Ingot 1S10A was rolled at 1000°C down to 30 mm thickness and rolled to the finished size (25 mm) at 900°C and produced an equiaxed grain size of 0.760 mm. The effect of holding time on grain size was investigated to determine the presence, if any, of a critical holding time, in the y loop, to produce grain refinement via the phase transformation (a - y). The results are shown in Figures 34 and 35.

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The possibility of grain refinement by thermal cycling through the a - y - a phase change was also investigated.

Ingot 1S20A was hot rolled at 1000°C down to 30 mm and rolled to 25 mm at 900°C and a final equiaxed grain size of 1.2 mm produced. The material was then cycled through the phase change up to five times, followed by an air cool. The results are shown in Figure 36.

It was considered that the lack of any tendency for this material to undergo grain refinement was due to the lack of fine second phase particles at the grain boundaries, and therefore no grain boundary pinning was evident. This was compounded by the use of high rolling temperatures required to avoid cracking during rolling. This also precluded the utilisation of strain energy in any heat treatment process.

TREATED2.1.2.1 ALUMINIUM.CASTS 'A-----

The addition of small quantities of aluminium powder together with a controlled amount of nitrogen (in stoichhnetric ratio) was made to two casts with a view to forming a fine dispersion of aluminium nitrides (see Table 2) in order to facilitate grain refinement.

Ingots 1505(2)A and 1510(2)A were inititally rolled to 30 mm flat at 1000°C and a finishing temperature of 900°C. The grain size achieved by this treatment was 1.4 mm and1.6 mm respectively. A charpy specimen of each material was fractured in liquid nitrogen at -196°C and examined in

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the SEM. No evidence of a fine dispersion of aluminium nitrides was observed. Subsequent examination of thin foils confirmed that no fine dispersion was present at the grain boundaries.

2.1.2.2 UPSET FORGING

In view of the large grain size and the restricted amount of deformation possible, by rolling, to achieve the finished specimen size, it was considered that a hot forging and rolling programme was required to obtain a greater proportion of deformation than by rolling alone.A number of trials were carried out to obtain the optimum conditions to produce a fine grain size. The final treatment involved the upset forging, to 50% deformation, in one pass at 1150°C followed by forging down to 27 mm flat and a final roll pass at 900°C to the finished size (25 mm).

Individual specimen blanks were subsequently heat treated at a series of temperatures and times to produce a uniform, varied grain size.

2.2. GRAIN SIZE MEASUREMENTS

Grain size measurements were made using a mean linear intercept technique145 . The method entails the measurement of the chord length defined by the intersection of a random straight line, by the grain boundaries on the plane of the polish. The mean linear intercept is then defined

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as d where:-

a = ± - 40n

where l is the length of the random line on the planar surface, and n is the number of grain boundary intersections on this line. The mean linear intercept is clearly less than the true grain size since it includes sectioning effects. The true mean diameter, D, is then defined as:-

D = 1.7 5 d - 41

The standard deviation of the mean is defined as:-

ad = SA - 42/IT

Where N is the number of observations made and a, is thedstandard deviation of the individual measurements. The relative error is then given by:-

a = — - 4 3d

The error of the individual intercept is given by:-

= 0.7 - 44Gda

and therefore the relative error is:-

a = Oil - 45vHT"

The grain size was determined in three directions to ensure that any non-uniformity of the grains was taken into

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consideration; determinations being made on broken test specimens in each case. The results of grain size measurements are given in Table 6.

2.3 TENSILE PROPERTIES

Tensile properties were obtained from test pieces of the geometry shown in Figure 37, machined from broken fatigue test specimens. The specimens were taken from positions indicated on Figure 38. It was considered that the removal of specimens from this position would negate the possibility of any influence of prior cyclic strain. The specimens were necessarily taken from a direction perpendicular to the applied stress in fatigue. Any differences in tensile properties due to the influence of orientation resulting from such a procedure were considered small since micro- structual evidence did not indicate the presence of any prefered orientation effects (see section 3.10).

The tests were carried out on a 500 kg capacity Instron universal testing machine (Model 1104). An Instron strain gauge extensometer, attached to the specimen, was used to obtain accurate values of proof stress. These results together with percentage elongation, reduction in cross- sectional area and the tensile strength are shown in Table 7. Large discrepancies between individual specimens from the same compact tension specimen may be as a result of the small ratio between tensile specimen diameter and grain size. This would result in small differences in microstructure having a disproportionate effect on tensile properties. These variations in the determination of

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tensile properties are also reflected in the calculation of plastic zone sizes (see table 9).

2.4 TEST PIECE PREPARATION

All fatigue crack growth tests were carried out using compact tension test pieces of a geometry shown in Figure 38. All specimen surfaces were ground finished and the faces metallographically polished to ensure ease of observation. Test piece dimensions were accurately determined before testing.

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2.5 CRACK GROWTH MEASURING TECHNIQUE

2.5.1 INTRODUCTION

The study of fatigue crack growth, and near threshold crack growth rates in particular, requires a sensitive and accurate technique for monitoring such growth. The correlation of fatigue crack growth rates with loading variables and metallographic features requires precise experimental procedures.

A fatigue crack growth monitoring technique must be capable of fulfilling the following requirements:-

(i) Be capable of operation over the long term periods necessary for threshold testing.

(ii) Not require visual accessiblity to the test pieceso that tests can be conducted under vacuum or other environments.

(iii) Must be capable of resolving small increments of crack growth.

(iv) Provide continuous measurement of crack length representative of the complete test piece thickness.

A number of experimental techniques have been used including ultrasonic and acoustic emission11*6 and X ray diffraction techniques11*7 but the DC potential drop technique best fits the above requirements11*8 151. This technique was used in this investigation. It must be noted that this technique provides no information about the shape of the crack front, because the PD response is measured across

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the notch and averaged through the thickness, or any deflection of the crack from the plane perpendicular to theapplied stress.

Essentially the technique involves passing a constant current through a cracked test piece under load, and measuring the potential difference across the crack. As the crack length increases, the area of uncracked ligament decreases, its resistance increases and the potential difference across the crack increases. The potential increase (V) is measured; from this and the known reference potential the crack lengthto test piece width can be determined.

2.5.2 CALIBRATION OF PD TECHNIQUE

In a current carrying body a disturbance in the potential field will exist around a discontinuity such as a crack.This is measured as the potential difference across the crack. If the body has homogeneous electrical properties and the current passing and temperature are held constant then there will be a unique relationship between the crack length and the potential difference across the crack for a given test peice geometry.

Calibrations may be produced theoretically, involving a solution of Laplace's equation

V2 U ) = 0 - 46

where V is the Laplacian operator cf> is the steady electrical potential or experimentally either by producing electrical analogues150 or by fatigue marking of real samples. In this investigation an experimental technique was used and

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is described below.

Theoretical calibrations involving a solution to Equation 42 which describes the electrical potential field in a geometry of specific boundary conditions for a specific test piece geometry are not easily applicable to complex test piece geometry although finite element analysis methods have been used152 and compare closely with those provided by experimental calibration for compact tension specimens.

2.5.3 EXPERIMENTAL CALIBRATION

Experimental calibrations may be made using thin foil analogues or by fatigue marking of real specimens and are conveniently represented in the form of variation of potential V/Vo with dimensionless crack length a/w.

Calibration was performed on test pieces identical to those used in threshold testing. Test piece surfaces were met- .alographically polished and marked at 1 mm intervals. As the fatigue crack reached each successive scribe mark the load was either raised or lowered to produce a marking on the fracture surface corresponding to the load change.Using this technique the position of the crack front can be fixed with respect to the potential associated with it.This procedure is continued until an a/w ratio of 0.75 is exceeded.

In practice this procedure did not produce a sufficiently

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well marked fracture surface, a problem which was overcome by interrupting the tests for periods to allow a film of oxide to form on the surface thus allowing easier identification of changes in load along the crack front.

Crack UrvjtVu measurements were averaged over values measured at 0, 25, 50, 75, 100% of the test piece thickness. The numerical average is taken as the characteristic crack length for subsequent analysis.

The calibration is represented by the dimensionless plot of the potential ratio V/Vo against dimensionless crack length a/W. This is show